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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* Copyright (C) 2002-2008 */
/* Romain BARDOU */
/* Jean-Franois COUCHOT */
/* Mehdi DOGGUY */
/* Jean-Christophe FILLITRE */
/* Thierry HUBERT */
/* Claude MARCH */
/* Yannick MOY */
/* Christine PAULIN */
/* Yann RGIS-GIANAS */
/* Nicolas ROUSSET */
/* Xavier URBAIN */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU General Public */
/* License version 2, as published by the Free Software Foundation. */
/* */
/* This software is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. */
/* */
/* See the GNU General Public License version 2 for more details */
/* (enclosed in the file GPL). */
/* */
/**************************************************************************/
/* Dijkstra's dutch flag */
//@+ CheckArithOverflow = no
/*@ predicate is_color(integer c) {
@ c == FlagStatic.BLUE || c == FlagStatic.WHITE || c == FlagStatic.RED
@ }
@*/
/*@ predicate is_color_array{L}(int t[]) {
@ t != null &&
@ \forall integer i; 0 <= i < t.length ==> is_color(t[i])
@ }
@*/
/*@ predicate is_monochrome{L}(int t[],integer i, integer j, int c) {
@ \forall integer k; i <= k < j ==> t[k] == c
@ }
@*/
class FlagStatic {
public static final int BLUE = 1, WHITE = 2, RED = 3;
/*@ requires t != null && 0 <= i <= j <= t.length ;
@ behavior decides_monochromatic:
@ ensures \result <==> is_monochrome(t,i,j,c);
@*/
public static boolean isMonochrome(int t[], int i, int j, int c) {
/*@ loop_invariant i <= k &&
@ (\forall integer l; i <= l < k ==> t[l]==c);
@ decreases j - k;
@*/
for (int k = i; k < j; k++) if (t[k] != c) return false;
return true;
}
/*@ requires 0 <= i < t.length && 0 <= j < t.length;
@ behavior i_j_swapped:
@ assigns t[i],t[j];
@ ensures t[i] == \old(t[j]) && t[j] == \old(t[i]);
@*/
private static void swap(int t[], int i, int j) {
int z = t[i];
t[i] = t[j];
t[j] = z;
}
/*@ requires
@ is_color_array(t);
@ behavior sorts:
@ assigns t[..];
@ ensures
@ (\exists int b r; is_monochrome(t,0,b,BLUE) &&
@ is_monochrome(t,b,r,WHITE) &&
@ is_monochrome(t,r,t.length,RED));
@*/
public static void flag(int t[]) {
int b = 0;
int i = 0;
int r = t.length;
/*@ loop_invariant
@ is_color_array(t) &&
@ 0 <= b <= i <= r <= t.length &&
@ is_monochrome(t,0,b,BLUE) &&
@ is_monochrome(t,b,i,WHITE) &&
@ is_monochrome(t,r,t.length,RED);
@ decreases r - i;
@*/
while (i < r) {
switch (t[i]) {
case BLUE:
swap(t,b++, i++);
break;
case WHITE:
i++;
break;
case RED:
swap(t,--r, i);
break;
}
}
}
}
/*
Local Variables:
compile-command: "make FlagStatic"
End:
*/
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